Analyses show that criticisms of CCSSM are incorrect. Research also provides guidelines for appropriate, effective, and joyful teaching and learning.

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- Author or Editor: Douglas H. Clements x

### Michael T. Battista and Douglas H. Clements

### Edited by Grayson H. Wheatley

Two second-grade students are investigating geometry with Logo. They are working in a TEACH environment in which the turtle-movement commands they enter are not only executed but simultaneously recorded in a procedure (Battista and Clements, in press; Clements 1983-84). During earlier lessons, they had successfully maneuvered the turtle to draw squares of various sizes. For each of these squares, they had used 90-degree turns. When asked how they knew whether a figure was a square, however, neither student had mentioned 90-degree turns.

### Grayson H. Wheatley and Douglas H. Clements

### Edited by Michael T. Battista

Many conflicting views have emerged about the place of calculators in elementary school mathematics. Some teachers and many parents believe that the use of calculators will undermine mastery of the “basic” and thus should not be used, at least until students “know their facts” and are proficient with paper-and-pencil computations. Others suggest that in today's society, facility with calculators is essential. The National Council of Teachers of Mathematics has, for many years now, held the position that calculators hould be used at all grade levels.

### Douglas H. Clements, David J. Whitin, Janet Bauman-Boatman and Gillian R. Clouthier

### Robert B. Davis, Douglas H. Clements and Michael T. Battista

Pupils often invent mathematical ideas and methods that go beyond what has been taught in class. The inventiveness is frequently noted in research studies based on careful observation of pupils talking about mathematical problem.

### Carolyn Kieran

### Edited by Michael T. Battista and Douglas H. Clements

Knowledge is not an entity which can be simply transferred from those who have to those who don't.… Knowledge is something which each individual learner must construct for and by himself. This view of knowledge as an individual construction … is usually referred to as constructivism. (Lochhead. cited in Blais 1988, 624)

### Leslie P. Steffe and John Olive

### Edited by Michael T. Battista and Douglas H. Clements

Researchers in Finland have warned for some years that children learn mathematics too mechanically in our comprehensive school. They learn rules and tricks. but not mathematical thinking. It is rote learning without meaning. I think this is what happens often with the fraction concept.